I would help on paper,..on computer...it 2 hard to type those functions,,,looks like grade 1o physics, i think
z^6+1=0 z^6=-1 z^6=e^i(PI+2nPI) i is imaginary number, PI is 3.14... is 180 degree z=e^i(PI/6+2nPI/6) z=Cos{PI/6 +2nPI/6} + i Sin{PI/6+2nPI/6} there are 6 roots by Letting n=0, n=1, n=2,..., n=5 Cos 3A = 4(CosA-Cos30)(CosA-Cos90)(Cos A -Cos 150) You know calculus, so this should be easy. Plug in and then simplify 4(....)(...)(...)=4(cosA)^3 - 3cosA =2cosA(1+cos2A)-3cosA =2cosAcos2A-CosA since (cosA)^2=(1+cos2a)/2 =cosAcos2A +cosAcos2A-cosA =CosAcos2A +cosA(1-2{sinA}^2) -cosA since cos2A=1-2(sinA)^2 =cosAcos2A-2(SinA)^2 cosA =cosAcos2A-sinA(2sinAcosA) =cosAcos2A-SinASin2A =cos 3A as desire.......... Since Cos(x+y)=CosxCosy-SinxSiny Now what's the magic word?
That seems right, but there is one thing that still confuses me. The way the question is worded, "deduce" would really be an indication that you're meant to use the previous part to help find the solution- given that it's a 'hence' question. I can see how that part works now, but I'm also trying to see if there is another way this problem can be solved where both parts are connected. I feel as though I'm just missing something in this question, as though there's a better/easier way. Of course, I'm basing this simply on the word "deduce". In physics, deduce usually means, "look you have pretty much got the answer, now read it off and copy down." And what magic word? I said thanks in advance in my initial post, didn't I? Calm down... he's just joking. No need to get defensive Double negatives. "I ain't no faggot" = "I am a faggot"
Thanks so much casshern! -hug r u guys serious? omg, what the ****..my MATH teacher gave these problems to me and plans on grading it as a test! i'm really annoyed now -_- neways, i would like to sincerely thank you again Casshern. I can tell you're really good at math. i didn't know i have such good, helpful PA friends. that means in the near future, i should have no problem asking for more help, right?
I'm just teasing, you shouldn't be ashamed if you don't fall into the stereotype. You know what they say, if you lack in one department means you must be talented in another. -cool
